Analytical solutions for the guided modes of rectangular silicon optical waveguides: a plane-wave approach

Marcatili’s analytical solution for the guided modes of rectangular optical waveguides (ROWGs) depends on (1) using the separation of variables (SOV) and (2) applying the paraxial approximation. It results in two classes of modes: the TE-like and the TM-like modes which are supported by these waveguides. These modes are uncoupled under low-index-contrast conditions. In the case of silicon-on-insulator (SOI) waveguides, the coupling between them can no longer be neglected. This paper extends using the SOV to find analytical modal solutions of SOI-ROWGs. It expands these solutions in quadruples of plane waves and develops a novel non-paraxial scattering model to account for the polarization coupling between these waves under high-index-contrast conditions. This model yields approximate analytical expressions of the field components of the guided modes which are the sum of major and minor Marcatili’s TE-like and TM-like modal fields. Numerical examples show excellent agreement with the field components of full-vectorial mode solvers.